AdvANCES iN NucLEAR SCiENCE ANd TECItNOLoGY VOLUME 19 Festschrift in Honor of Eugene P. Wigner AdvANCES iN NucLEAR SCiENCE ANd TECItNOLoGY Series Editors Jeffery Lewins Fellow of Magdalene College Cambridge University, Cambridge, England Martin Becker Rensselaer Polytechnic Institute, Troy, New York Editorial Board Eugene P. Wigner, Honorary President R. W. Albrecht F. R. Farmer Ernest J. Henley Norman Hilberry John D. McKean K. Oshima A. Sesonske H. B. Smets Karl Wirtz C. P. L. Zaleski A Continuation Order Plan is available for this series. A continuation order will bring delivery of each new volume immediately upon publication. Volumes are billed only upon actual shipment. For further information please contact the publisher. AdvANCES iN NucLEAR SCiENCE ANd TECItNOLoGY VOLUME 19 Festschrift in Honor of Eugene P. Wigner Edited by Jeffery Lewins Fellow of Magdalene College Cambridge University Cambridge, England and Martin Becker Rensselaer Polytechnic Institute Troy, New York PLENUM PRESS, NEW YORK AND LONDON The Library of Congress has cataloged this title as follows: Advances in nuclear science and technology. v. 1- 1962- New York, Plenum Press [etc.] v. ill., diagrs. 24 cm. Annual. Editors: 1962-66 E. J. Henley and H. Kouts; 1968- E. J. Henley and others. ISSN 0065-2989 = Advances in nuclear science and technology. 1. Nuclear engineering-Yearbooks. 2. Nuclear physics-Yearbooks. I. Henley, Ernest J., ed. II. Kouts, Herbert, 1919- ed. [DNlM: W1 AD685] TK9001.A3 621.48058 62-13039 MARC-S Library of Congress [8412] ISBN-13: 978-1-4684-5301-0 e-ISBN-13: 978-1-4684-5299-0 001: 10.1007/978-1-4684-5299-0 © 1987 Plenum Press, New York Softcover reprint of the hardcover 1st edition 1987 A Division of Plenum Publishing Corporation 233 Spring Street, New York, N.Y. 10013 All rights reserved No part of this book may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording, or otherwise, without written permission from the Publisher Frontispiece: Eugene P. Wigner PREFACE Our volume in the annual review series on this occasion represents a departure from our usual practice in that it serves as a Festschrift for Eugene Wigner. Dr. Wigner has won many honours in his long, wide ranging and distinguished career spanning so many upheavals in civilized life. The editors and the authors, indeed the whole nuclear engineering community, will wish to join in a modest but further acknowledgement of the contributions he has made to nuclear engineering, not least to the morality and professionalism of nuclear engineering in a year that has raised such international concerns over safety. It suffices to make a bald statement of Eugene Wigner's life and times here, for the first article of the volume is a loving appreciation by his long-time colleague, Alvin Weinberg, an evaluation of his contribution historically during and after the Second World War but equally an account of the philosophy which Wigner provided to the burgeoning profession. Eugene Wigner was born 17th November, 1902 in Budapest, Hungary and his early schooling is described by Dr. Weinberg. In the upheavals of the 'thirties, he came to the u.S. to start a long association with Princeton, 1930-1971, originally as a part time Professor of Mathematics and with extended periods of leave to further other matters. Thus he was at the Metallurgical Laboratory (Plutonium Project), University of Chicago 1942-45, Director of Research and Development at the Clinton Laboratories, Oak Ridge 1945-46 and returned to Oak Ridge as Director of the Civil Defence Project 1964-65. His honours and distinctions are numerous and the following but a partial list: Franklin Medal, 1950; Fermi Award, 1958; Atoms for Peace Award, 1960; Max Planck Medal, 1961; Nobel Prize for Physics, 1963; U.S. National Medal for Science, 1969; Albert Einstein Award, 1972 and of course the first Wigner Medal, 1978. vO viii PREFACE The balance of our Festschrift is provided by an inter national authorship who bring us modern accounts of some of the developments initiated by Wigner. One of the curiosities of the linear (neutron) transport theory was the late realisation that it would yield to conventional eigenfunction solution, albeit involving singular integrals and a continuous spectrum of eigenvalues for this integro-differential model. Wigner and Boris Davison had both identified a need to look more closely at the mathematical structure and after the War Wigner found time to work out the details, although these are probably better known now from the devoted work of Case and Zweifel together with their school. In this volume, Professor R. T. Ackroyd and his colleagues in What may be called the English school provides a similar theoretical treatment, using the variational method (another of Wigner's contributions to nuclear engineering) to display the nature of the finite element method as applied today in reactor physics calculations. The basis of the transport operator in a variational principle is a powerful technique we need not elaborate in the Preface. When this is to be associated with a least squares error measure, then the relation to a non-self adjoint operator is for consideration if the stationary condition is to be a minimum condition having the desired Euler-Lagrange equations. We recall a personal experience when one of us gave an early public paper and the figure rising at the back of the Hall proved to be that of Professor Wigner with a question or rather, a comment; no little occasion to try the nerves of a young lecturer. A propos of Ackroyd's treatment of the A*A operator made thus self-adjoint, Eugene Wigner started by saying "It is a well known fact ... " and then paused, until resuming with his unswerving accuracy "It is well known to some people that every operator can be made self-adjoint". As Weinberg pOints out, a major thrust of Wigner's philosophy was toward an inherently safe reactor. The volume continues with two up to date accounts of how this philosophy is seen to be accomplished, one from Europe and one from the United States. Dr. Hannerz has given us a description of the PIUS system now offered from Sweden with its ingenious use of hydraulic-thermal locks to provide for automatic supply of cooolant in any excursion. The PRISM reactor described by Dr. Pluta puts more emphasis on the modular nature of the system, the opportunity to dissociate the balance of plant from the nuclear island with its more severe safety require- PREFACE ix ments and the appealing financial implications of bringing a multiple station on line early before interest rates cripple the project. Surely there are other techniques to exploit to promote inherent safety. One recollects the advocacy of Teller for the underground reactor. The experience of the Swiss with their experimental reactor accident suggests that much may be gained by guaranteeing containment. With modern drilling techniques, a reactor vault 300 m underground is readily constructed. It may also be argued as economic if it obviates a number of features required in any surface contain ment. The obvious further development is for the self contained i.e. fuel manufacturing and reprocessing plant. Here the original interest of the chemical engineer in Wigner may also be reexploited to provide on-line fuel processing rather than the mechanical engineer's route to the nuclear system. There is, by the way, in the U.K., an 8000 MWe generation plant hollowed out within a Welsh mountain, at the Dinorwic pumped storage plant which testifies to the practicability of underground containment of generating plant. We have already mentioned the introduciton of variational methods or more particularly non-self adjoint perturbation methods in nuclear engineering by Eugene Wigner. It is appropriate therefore to include in this volume of homage a general treatise on the generalised perturbation method that has sprung from the seed Wigner sowed in discussing the Fermi-age equation. Professor Gandini brings to such a review his lifelong interest in the method, showing how it applied to both continuum and discrete models and therefore to a wide range of engineering phenomena. The extension to higher order methods greatly enhances the computational effectiveness of perturbation theory. Finally the editors wish to acknowledge the benefit the series has had in its Editorial Board of which Eugene Wigner has been a member since the start (in 1962) and of which he is now our Honorary President. Authors and Editors join with Alvin Weinberg in offering this volume in love and gratitude to a physicist, chemist and mathematician, to a distinguished nuclear scientist, engineer and philosopher, Eugene Paul Wigner. August, 1986 J. D. Lewins M. Becker CONTENTS Eugene Wigner and Nuclear Energy A. M. Weinberg I. Introduction 1 II. The Pre-Chicago Days 3 III. Chicago Metallurgical Laboratory 5 IV. Clinton Laboratories, 1946-47 . 13 V. Reactor Physics and General Engineering 16 VI. Macroscopic Reactor Theory 17 VII. Temperature Effects: The Wigner-Wilkins Distribution 20 VIII.Solid State Physics . 21 IX. Nuclea.r physics at Chicago and Clinton 21 X. General Energy policy 22 XI. Civil Defence 23 XII. Wigner and the Founding of ORNL 24 XIII. Eugene Wigner and Nuclear Energy 25 XIV. Annotated Bibliographies 27 References 39 The PIUS Principle and the SECURE Reactor Concepts KOre Hannerz I. Introduction 41 II. Design Goals for "Forgiving" LWRs 43 III. The PIUS Design Principle 45 IV. System Modelling 51 V. Design Implementation 54 VI. The Nuclear Power Reactor SECURE-P 55 VII. The Heat Producing Reactor SECURE-H 97 VIII.The Low Temperature Heating Reactor SECURE-LH . 103 IX. Concluding Remarks 104 References 107 xi xii CONTENTS PRISM: An Innovative Inherently Safe Modular Sodium Cooled Breeder Reactor P. R. Pluta, F. E. Tippets, R. E. Murata, C. E. Boardman, C. S. Schatmeir, A. E. Dubberley, D. M. Switick, W. Kwant I. Introduction 109 II. Overall Plant Description 110 III. Reactor Assembly and Support Structures 133 IV. Heat Transport and Power Generation Systems 161 V. Shutdown Heat Removal Systems 167 VI. PRISM Inherent Safety Characteristics 174 VII. Concept Summary and Implementation Strategy 193 Acknowled0ement 202 References 202 Generalised Perturbation Theory (GPT). A Heuristic Approach A. Gandini I. Introduction 205 II. GPT Methodology for Linear Systems 208 III. GPT Methodology for Nonlinear Systems 262 IV. Fields of Interest 276 V. Expansion of the Perturbed Field Function 335 VI. Final Remarks 344 Appendix 1: Frechet Derivatives • 347 Appendix 2: Second Order GPT Critical Systems Expressions · 352 Appendix 3: Discretised Systems . • 354 Appendix 4: The Importance Function in the Enthalpy Field · 356 Appendix 5: Miscellaneous Arguments Relevant to GPT . · 364 Appendix 6: Alternative Derivatrion in Temperature Field 373 References 375